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IssuesArchive of Issues2001-6pp.91-96

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A. V. Gnoevoi, D. M. Klimov, and V. M. Chesnokov, "On the equations of flow of Bingam media," Mech. Solids. 36 (6), 91-96 (2001)
Year 2001 Volume 36 Number 6 Pages 91-96
Title On the equations of flow of Bingam media
Author(s) A. V. Gnoevoi (Moscow)
D. M. Klimov (Moscow)
V. M. Chesnokov (Moscow)
Abstract A system of equations is obtained for analyzing the flow of Bingam media. The difference of this system from systems obtained previously is that only one equation - the basic rheological law of deformation of the medium - contains an ambiguity. This ambiguity is eliminated from the rheological equation by using either physical considerations or mechanical formulation of the problem. The equations obtained permit one to investigate the flow of a Bingam medium in the entire region of flow, i.e., in the regions of both shear and plastic flows. Particular cases of these equations are the equations of flow of viscous media (Newton's fluids) and ideally plastic media. These particular cases are obtained from the general equations by equating appropriate rheological constants to zero. As an example, the equations obtained are used for analyzing the flow of a Bingam medium between parallel plates under a prescribed pressure differential.
References
1.  L. M. Kachanov, Fundamentals of the Theory of Plasticity [in Russian], Nauka, Moscow, 1969.
2.  B. Saint-Venant, "On the determination of the equations of internal motions occurring in plastic solids beyond the elastic limit," in Yu. N. Rabotnov (Editor), Theory of Plasticity. Collected Papers [Russian translation], pp. 11-19, Izd-vo Inostr. Lit-ry, Moscow, 1948.
3.  M. Levi, "To the general equations of internal motions occurring in plastic solids beyond the elastic limit," in Yu. N. Rabotnov (Editor), Theory of Plasticity. Collected Papers [Russian translation], pp. 20-23, Izd-vo Inostr. Lit-ry, Moscow, 1948.
4.  A. V. Gnoevoi, D. M. Klimov, and V. M. Chesnokov, To the Theory of Flow of Bingam Media. Preprint No. 626 [in Russian], Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow, 1998.
5.  A. V. Gnoevoi, D. M. Klimov, and V. M. Chesnokov, "On one case of the plane flow of Bingam media," Izv. AN. MTT [Mechanics of Solid], No. 5, pp. 63-73, 2001.
6.  N. A. Slezkin, Dynamics of a Viscous Incompressible Fluid [in Russian], Gostekhizdat, Moscow, 1955.
7.  M. Reiner, Deformation and Flow [Russian translation], Gostoptekhizdat, Moscow, 1963.
8.  H. Henky, "On the slow steady-state flows in plastic bodies with applications to rolling, pressing, and drawing," in Yu. N. Rabotnov (Editor), Theory of Plasticity. Collected Papers [Russian translation], pp. 136-156, Izd-vo Inostr. Lit-ry, Moscow, 1948.
9.  M. P. Volarovich and A. M. Gutkin, "Flow of a viscoplastic body between two parallel plane walls and an annular clearance between coaxial tubes," ZhTF, Vol. 16, No. 3, pp. 321-329, 1946.
Received 18 September 2000
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